Number Of Possible Allocations Research Articles

Deep Reinforcement Learning for One-Warehouse Multi-Retailer inventory management

The One-Warehouse Multi-Retailer (OWMR) system is the prototypical distribution and inventory system. Many OWMR variants exist, e.g. demand in excess of supply may be completely back-ordered, partially back-ordered, or lost. Prior research has focused on the study of heuristic reordering policies such as echelon base-stock levels coupled with heuristic allocation policies. Constructing well-performing policies is time-consuming and must be redone for every problem variant. By contrast, Deep Reinforcement Learning (DRL) is a general purpose technique for sequential decision making that has yielded good results for various challenging inventory systems. However, applying DRL to OWMR problems is nontrivial, since allocation involves setting a quantity for each retailer: The number of possible allocations grows exponentially in the number of retailers. Since each action is typically associated with a neural network output node, this renders standard DRL techniques intractable. Our proposed DRL algorithm instead inferences a multi-discrete action distribution which has output nodes that grow linearly in the number of retailers. Moreover, when total retailer orders exceed the available warehouse inventory, we propose a random rationing policy that substantially improves the ability of standard DRL algorithms to train good policies because it promotes the learning of feasible retailer order quantities. The resulting algorithm outperforms general-purpose benchmark policies by ∼1−3% for the lost sales case and by ∼12−20% for the partial back-ordering case. For complete back-ordering, the algorithm cannot consistently outperform the benchmark.

Optimal Allocation of the COVID-19 Stimulus Checks

Congress spent $250B sending stimulus checks to individuals. Could the same stimulus have been achieved for less, assuming the government’s information is restricted to 2019 tax returns? Using a life-cycle consumption-saving model with heterogeneous consumers, we calculate the consumption responses to $100 increments of cash transfers by, e.g., marital status, income, and number of children. We find the optimal allocation under different constraints using a new algorithm that can rank an arbitrarily-large number of possible allocations. The optimal policy roughly doubles the amount for low-income and younger consumers and can achieve the same stimulus at almost half the cost.

Explaining the variation in the attained power of a stepped-wedge trial with unequal cluster sizes

BackgroundIn a cross-sectional stepped-wedge trial with unequal cluster sizes, attained power in the trial depends on the realized allocation of the clusters. This attained power may differ from the expected power calculated using standard formulae by averaging the attained powers over all allocations the randomization algorithm can generate. We investigated the effect of design factors and allocation characteristics on attained power and developed models to predict attained power based on allocation characteristics.MethodBased on data simulated and analyzed using linear mixed-effects models, we evaluated the distribution of attained powers under different scenarios with varying intraclass correlation coefficient (ICC) of the responses, coefficient of variation (CV) of the cluster sizes, number of cluster-size groups, distributions of group sizes, and number of clusters. We explored the relationship between attained power and two allocation characteristics: the individual-level correlation between treatment status and time period, and the absolute treatment group imbalance. When computational time was excessive due to a scenario having a large number of possible allocations, we developed regression models to predict attained power using the treatment-vs-time period correlation and absolute treatment group imbalance as predictors.ResultsThe risk of attained power falling more than 5% below the expected or nominal power decreased as the ICC or number of clusters increased and as the CV decreased. Attained power was strongly affected by the treatment-vs-time period correlation. The absolute treatment group imbalance had much less impact on attained power. The attained power for any allocation was predicted accurately using a logistic regression model with the treatment-vs-time period correlation and the absolute treatment group imbalance as predictors.ConclusionIn a stepped-wedge trial with unequal cluster sizes, the risk that randomization yields an allocation with inadequate attained power depends on the ICC, the CV of the cluster sizes, and number of clusters. To reduce the computational burden of simulating attained power for allocations, the attained power can be predicted via regression modeling. Trial designers can reduce the risk of low attained power by restricting the randomization algorithm to avoid allocations with large treatment-vs-time period correlations.

Optimal Treatment Allocations in Space and Time for On-Line Control of an Emerging Infectious Disease

A key component in controlling the spread of an epidemic is deciding where, when and to whom to apply an intervention. We develop a framework for using data to inform these decisions in realtime. We formalize a treatment allocation strategy as a sequence of functions, one per treatment period, that map up-to-date information on the spread of an infectious disease to a subset of locations where treatment should be allocated. An optimal allocation strategy optimizes some cumulative outcome, e.g. the number of uninfected locations, the geographic footprint of the disease or the cost of the epidemic. Estimation of an optimal allocation strategy for an emerging infectious disease is challenging because spatial proximity induces interference between locations, the number of possible allocations is exponential in the number of locations, and because disease dynamics and intervention effectiveness are unknown at out-break. We derive a Bayesian on-line estimator of the optimal allocation strategy that combines simulation-optimization with Thompson sampling. The estimator proposed performs favourably in simulation experiments. This work is motivated by and illustrated using data on the spread of white nose syndrome, which is a highly fatal infectious disease devastating bat populations in North America.

Implications of the assumptions on which the p -median problem are based when distribution network design

Abstract In a previous work, a real distribution network is optimized with a heterogeneous fleet minimizing the costs involved, which decision variables are: location, allocation, routing and inventory. To optimize the distribution network a methodology of three phases was proposed: location, allocation, routing and routing-inventory. In each phase models and algorithms to their optimization were proposed, specifically the phases one and two are detailed. In phase one, the p-median was used in order to localize the distribution centres and in phase two, i.e. the customer allocation to the distribution centres, cheaper costs were used in addition to the real characteristics of non-urban road network. In this optimization process a finding of great importance was found: the solution spaces to be evaluated of the p-median problem applied to a real problem is not exponential but rather the opposite, the solution space is finite numerals as well as the number of possible allocations carried out by each of the allocated distribution centre. In this work is shown empirically that the number of scenarios to be evaluated for the localization of the distribution centres and the customer allocation them is not exponential.

서비스 고정비용을 고려한 복수제품 선별검사와 서비스시스템 설계

In this paper, we design sampling inspections and service capacities simultaneously for multi-products. Products are supplied in batches after rectifying inspections, that is, rejected lot is subject to total inspection and defective products are reworked to good ones. When supplied, all defective products are uncovered and returned to service. Particularly, we extend Kim [1] by introducing the fixed costs of providing services and show that the cost function of a product is no longer linear or convex in terms of the level of service provision. We develop a framework for a product to deal with this joint design problem and a dynamic programming algorithm for multi-products which allocates the given number of the total service capacities among products with the considerably smaller computations than the total number of possible allocations.

Load allocation problem for optimal design of aircraft electrical power system

More and more electric systems are embedded in today aircraft. As a result, the complexity of electrical power system design is increasing and the need of generic and efficient design methods is today required. Among numerous design tasks, the allocation of electric systems on the busbars of the electrical power system is considered as an important one since it has a direct impact on the aircraft mass. But due to the high number of possible allocations and regarding the large diversity of potential sizing cases for the equipments, finding the optimal allocation of electric loads is a hard task. In this paper, the problem is formalized mathematically. Then, four stochastic optimization methods are assessed on complex load allocation problems. Based on this assessment, a genetic algorithm using niching method is considered as the most appropriate algorithm for solving this aircraft design problem

A method to search for optimal field allocations of transgenic maize in the context of co-existence

Spatially isolating genetically modified (GM) maize fields from non-GM maize fields is a robust on-farm measure to keep the adventitious presence of GM material in the harvest of neighboring fields due to cross-fertilizations below the European labeling threshold of 0.9%. However, the implementation of mandatory and rigid isolation perimeters can affect the farmers' freedom of choice to grow GM maize on their fields if neighboring farmers do not concur with their respective cropping intentions and crop plans. To minimize the presence of non-GM maize within isolation perimeters implemented around GM maize fields, a method was developed for optimally allocating GM maize to a particular set of fields. Using a Geographic Information System dataset and Monte Carlo analyses, three scenarios were tested in a maize cultivation area with a low maize share in Flanders (Belgium). It was assumed that some farmers would act in collaboration by sharing the allocation of all their arable land for the cultivation of GM maize. From the large number of possible allocations of GM maize to any field of the shared pool of arable land, the best field combinations were selected. Compared to a random allocation of GM maize, the best field combinations made it possible to reduce spatial co-existence problems, since at least two times less non-GM maize fields and their corresponding farmers occurred within the implemented isolation perimeters. In the selected field sets, the mean field size was always larger than the mean field size of the common pool of arable land. These preliminary data confirm that the optimal allocation of GM maize over the landscape might theoretically be a valuable option to facilitate the implementation of rigid isolation perimeters imposed by law.

Nearly Optimal Allocation of Experimental Units Using Observed Covariate Values

In many of the experimental situations to which the analysis-of-covariance model applies, the values of the covariates are known prior to the actual experiment so that they can be used in allocating the experimental units to the treatments. Due to the large number of possible allocations, the computation of an allocation that is D-optimal for inferences on the treatment means will generally not be practical. Good allocations can be constructed by a multistage procedure that allocates one or more units at each stage. These allocations can be made even better by applying an iterative algorithm that induces small changes in the design at each iteration. The techniques were applied to an example taken from the chemical industry and produced highly efficient allocations. Similar design techniques can be used in experimental situations where the experimental units become available and must be allocated in stages.